THE ARMS RACE in the New York subway system has not escalated so far, which is a great relief to the beleaguered authorities. There have been muggings since Dec. 22, the day that Bernhard Goetz shot his way into history by allegedly gunning down four teen-agers who surrounded him and asked for money, evidence that New Yorkers, many of whom want to give Goetz a ticker-tape parade, are not yet following his example and packing guns for the daily commute.

Goetz has become the most talked- about man in America. He is not, he told a friend while awaiting arraignment in New York, "a hero." But he is to those who feel that things are out of control in the city, particularly underground, in what has been called "Dante's Fifth Circle of Hell."

Goetz is a slight, pale, solitary electronics expert, hardly your stereotyped vigilante. For threatened, powerless people, he is the avenger, the victim who struck back. His action lit a bonfire of public passion against "police who can't protect the citizens, patsy judges and prosecutors who plea-bargain away 90 per cent of their cases."

For the elderly who dare not leave their homes, for every man or woman who felt the humiliation and outrage of being mugged on their own streets, he represents satisfaction, and a kind of restitution.

Probably not since Lt. William Calley was court-martialed for the Mylai massacre has there been such an outcry in favor of an individual who committed an act of violence.

While Goetz was in flight, the police hotline set up to encourage tipsters was flooded with furious calls from New Yorkers who said they hoped the police would never find him, gave their names and said that Goetz should not be caught, but congratulated. Checks are still coming in for his defense, from all over the country, from people who rejoice that the Big Apple, the home of liberal do-goodism, has been exposed in all its rottenness.

President Reagan said all the right things at his press conference about not condoning what Goetz did. But it gave Reagan a chance to take a dig at the wrong-headed philosophy that led to a situation where it "seemed that we got overzealous about protecting the criminal's rights and forgot about the victim."

The ambivalence about the case crosses racial lines -- the victims were all black, with police records -- but black civil rights leader Roy Innis offered legal help, and the mother of one of the victims said that Goetz's bullet might stop her son in his tracks -- she couldn't. The first reaction even among the most militantly non- violent was, alas, "Hooray" followed by sheepish second thoughts.

Goetz is an object of world-wide fascination. Television crews from London, Stockholm and Japan follow him.

Now Governor Mario Cuomo and Mayor Edward J. Koch, who are feeling the heat of citizen fury, are trying to persuade people that while they can understand and sympathize with Goetz, they must not emulate him in taking the law into their own hands.

People who say that Goetz over- reacted -- or as the law says, used excessive force to meet a threat -- are shouted down at social gatherings. Much can be said for him. No Manhattan subway passenger could imagine that a refusal to give four teen-agers five dollars on demand would produce anything but the use of the screwdrivers they had in their pockets.

Paranoia is difficult to charge. Goetz had been robbed before, in January, 1981. His impaired confidence in the system of justice is understandable. The charge against his assailant was dropped to "simple assault." While the offender was out on bail, he committed three other armed robberies, and is currently serving a sentence which could end in three years.

If Goetz ever goes to trial, he is expected to plead self-defense. The New Hampsire authorities to whom he surrendered indicated possible "pre-meditation."

He may never go to trial, since the four victims have declined to testify -- one of them, who was paralyzed from the waist down from his wound, couldn't in any case, since he is in a coma.

Court officials appreciate the difficulties of getting a jury, and, even more, in the present climate, a conviction.

It won't do to tell New Yorkers that their city actually ranks 10th in serious crime, or that millions of passengers safely ride the world's largest, and grimiest subway system.

"You can't wave a printout at them when they think you're somebody who rides a car to work," says Ken Conboy, who, as the city's coordinator of criminal justice, is in the eye of the storm. "They think teen-agers roam the subways tormenting people with impunity."

Governor Cuomo and Mayor Koch, who share responsbility for the transportation system, are exhorting citizens to remember that they are members of a civilized society. Goetz's violent action and the primal rage it has stirred, seem, unfortunately, to have put the burden of proof on them.